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  {
   "cell_type": "code",
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   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.optimize import leastsq\n",
    "\n",
    "def Fun(p,x):                        # 定义拟合函数形式\n",
    "    a1,a2,a3 = p\n",
    "    return a1*x**2+a2*x+a3\n",
    "\n",
    "def error (p,x,y):                   # 拟合残差\n",
    "    return Fun(p,x)-y "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = np.linspace(-10,10,100)           # 创建时间序列\n",
    "p_value = [-2,5,10]                   # 原始数据的参数\n",
    "noise = np.random.randn(len(x))       # 创建随机噪声\n",
    "y = Fun(p_value,x)+noise*2            # 加上噪声的序列"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
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     },
     "metadata": {
      "needs_background": "light"
     }
    },
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "[-2.01055415  5.01727851 10.40251024]\n"
     ]
    }
   ],
   "source": [
    "p0 = [0.1,-0.01,100] # 拟合的初始参数设置\n",
    "para =leastsq(error, p0, args=(x,y))  # 进行拟合\n",
    "y_fitted = Fun (para[0],x)            # 画出拟合后的曲线\n",
    "plt.figure\n",
    "plt.plot(x,y,'r', label = 'Original curve')\n",
    "plt.plot(x,y_fitted,'-b', label ='Fitted curve')\n",
    "plt.legend()\n",
    "plt.show()\n",
    "print (para[0])"
   ]
  },
  {
   "source": [
    "#use curve_fit() function to solve this problem"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "text/plain": "<Figure size 432x288 with 1 Axes>",
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     },
     "metadata": {
      "needs_background": "light"
     }
    },
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "[-2.00288231  5.04747886 10.23866493]\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.optimize import curve_fit\n",
    " \n",
    "def Fun(x,a1,a2,a3):                   # 定义拟合函数形式\n",
    "    return a1*x**2+a2*x+a3\n",
    "def error (p,x,y): # 拟合残差\n",
    " return Fun(p,x)-y\n",
    "\n",
    "x = np.linspace(-10,10,100)       # 创建时间序列\n",
    "a1,a2,a3 = [-2,5,10]              # 原始数据的参数\n",
    "noise = np.random.randn(len(x))   # 创建随机噪声\n",
    "y = Fun(x,a1,a2,a3)+noise*2       # 加上噪声的序列\n",
    "para,pcov=curve_fit(Fun,x,y)\n",
    "y_fitted = Fun(x,para[0],para[1],para[2]) # 画出拟合后的曲线\n",
    "\n",
    "plt.figure\n",
    "plt.plot(x,y,'r', label = 'Original curve')\n",
    "plt.plot(x,y_fitted,'-b', label ='Fitted curve')\n",
    "plt.legend()\n",
    "plt.show()\n",
    "print (para)"
   ]
  },
  {
   "source": [
    "Polynomial fitting"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    },
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "[-2.00832696  4.99960921 10.16586388]\n"
     ]
    }
   ],
   "source": [
    "x = np.linspace(-10,10,100) # 创建时间序列\n",
    "a1,a2,a3 = [-2,5,10] # 原始数据的参数\n",
    "noise = np.random.randn(len(x)) # 创建随机噪声\n",
    "y = Fun(x,a1,a2,a3)+noise*2 # 加上噪声的序列\n",
    "plt.plot(x,y)\n",
    "para=np.polyfit(x, y, deg = 2)\n",
    "\n",
    "y_fitted = Fun(x,para[0],para[1],para[2])\n",
    "plt.figure\n",
    "plt.plot(x,y,'ro', label = 'Original curve')\n",
    "plt.plot(x,y_fitted,'-b', label ='Fitted curve')\n",
    "plt.legend()\n",
    "plt.show()\n",
    "print(para)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ]
}